Stretching yardstick II: Photometric Paradox

This is a continuation of my previous post.

If we assume that the Universe is infinite, stationary and evenly filled with stars, then the number of stars at distance about from Earth is proportional to , while intensity of light from them declines as . Hence contribution of stars at distance to the brightness of our skies does not depend on and positive, hence the brightness of the sky has to be infinite. This is the famous Dark Sky Paradox, or Photometric Paradox — its history can be traced, apparently, back to Kepler.

Revisiting the snail on the rubber tape of the previous post — what will happen with the brightness of our skies if the universe was infinite, uniformly filled with stars, but non-stationary and, instead, uniformly expanding?